Theo vi-et ta có: \(\hept{\begin{cases}x_1+x_2=-2\left(m+1\right)\\x_1x_2=2m^2+9m+7\end{cases}}\)
Theo đề bài ta có:
\(\left|\frac{7\left(x_1+x_2\right)}{2}-x_1x_2\right|\le18\)
\(\Leftrightarrow\left|\frac{7\left(-2\left(m+1\right)\right)}{2}-\left(2m^2+9m+7\right)\right|\le18\)
\(\Leftrightarrow\left|-2m-16m-14\right|\le18\)
Xét VT ta có:
| - 2m2 - 16m - 14| = | ( - 2m2 - 16m - 32) + 18|
= |- 2(m + 4)2 + 18| \(\le\)|18| = 18